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Block #1,113,480

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/17/2015, 4:42:49 PM Β· Difficulty 10.9052 Β· 5,725,907 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
282b78ee6a40aa5937f0903c21f993800fca3be6081e6313dc643db2d63b8794
View on Chainz β†—

Height

#1,113,480

Difficulty

10.905227

Transactions

1

Size

207 B

Version

2

Bits

0ae7bcef

Nonce

2,829,897,258

Timestamp

6/17/2015, 4:42:49 PM

Confirmations

5,725,907

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

e280579c2beb3a36c03189467bce3bfe3988fe37aca53703842834930ef169e5
Transactions (1)
Coinbasee280579c2beb3a…2834930ef169e5
1 in β†’ 1 out8.4000 XPM116 B
AJCEY9yy…tg97E6zm
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.014 Γ— 10⁹⁢(97-digit number)
10143995940422278756…36869064795828161921
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
1.014 Γ— 10⁹⁢(97-digit number)
10143995940422278756…36869064795828161921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.028 Γ— 10⁹⁢(97-digit number)
20287991880844557513…73738129591656323841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.057 Γ— 10⁹⁢(97-digit number)
40575983761689115026…47476259183312647681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.115 Γ— 10⁹⁢(97-digit number)
81151967523378230053…94952518366625295361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.623 Γ— 10⁹⁷(98-digit number)
16230393504675646010…89905036733250590721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.246 Γ— 10⁹⁷(98-digit number)
32460787009351292021…79810073466501181441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.492 Γ— 10⁹⁷(98-digit number)
64921574018702584042…59620146933002362881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.298 Γ— 10⁹⁸(99-digit number)
12984314803740516808…19240293866004725761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.596 Γ— 10⁹⁸(99-digit number)
25968629607481033617…38480587732009451521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.193 Γ— 10⁹⁸(99-digit number)
51937259214962067234…76961175464018903041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.038 Γ— 10⁹⁹(100-digit number)
10387451842992413446…53922350928037806081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
2.077 Γ— 10⁹⁹(100-digit number)
20774903685984826893…07844701856075612161
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,959,380 XPMΒ·at block #6,839,386 Β· updates every 60s
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